In classical electrodynamics (CED), the most important quantities are the electric and magnetic fields, which directly determine the forces. In quantum electrodynamics (QED), the potentials are the most important quantities; they determine the energy and momentum exchange between the EM field and matter. Gauge invariance, which in CED is just a mathematical curiosity, becomes fundamental in QED, ruling the gauge symmetry that determines the interaction itself.

The Lamb experiment that opened the way is discussed in detail.

Feynman diagrams are graphic representations of mathematical expressions of scattering or decay amplitudes. Without going into the mathematics, we use them to visually suggest the underlying physics. We show how the propagator describes virtual particles, and how uncertainty and relativity principles, joined, imply the existence of antimatter.

The fine-structure constant, which is the dimensionless expression of the electromagnetic charge, depends on the momentum transfer between the probe and the target charge in the scattering experiment we are performing. The ‘running’ of the coupling constants is a property of all the interactions.

The highest precision measurements and theoretical predictions of the magnetic moments of the electron and of the muon. The precision frontier to search for new physics.

This chapter introduces the formal second quantization method for fermions in quantum field theory, and the connection to second quantization of bosons is shown. The picture of fermions as rotations between two states is presented, which helps the reader to see where the Pauli exclusion rule comes from. Finally, Dirac’s original derivation of his equation for relativistic motion of fermions is given.

This chapter gives a brief but quantitative introduction to the method of Feynman diagrams in quantum field theory, sufficient for the reader to understand what these diagrams mean. The concept of “vacuum energy” is discussed in this context.

This chapter gives a quantitative introduction to decoherence theory, including density matrix formalism in the context of quantum field theory, and a survey of the quantum trajectories method. Finally, the mathematical structure for a new proposal for spontaneous collapse, introduced nonmathematically in Chapter 6, is given.

This chapter shows how particles arise naturally as an effect of waves, known as “resonance,” and that the particle concept, properly understood, is not somehow incompatible with the existence of waves. The definitions of “fermion” and “boson” fields, often associated with “matter” and “energy” particles, are introduced. The solidness of objects in our experience is a direct consequence of fermion wave properties.

This chapter introduces the formal “second quantization” method for bosons in quantum field theory. It is shown that phonons (sound particles) and photons (light particles) are simple extensions of the physics of a spring-like oscillator. The connection of boson states to classical waves is shown in a discussion of “coherent states.”

This chapter begins a five-chapter mathematical introduction to quantum field theory, appropriate for upper-level undergraduate science or engineering students, or those with some mathematical training who would like to know what the “real” theory of quantum mechanics is. In this chapter, the basics of Dirac notation are presented. The last part of this chapter shows how the uncertainty principle of quantum mechanics is derived.

This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.

This chapter explains what we mean by “fields” and “waves” in physics, and argues that quantum waves are just as “real” as other waves we experience in daily life, such as water waves and sound waves.

There are many representations of time reversal symmetry, including PT, CT, and CPT, but only the standard time reversal operator T is associated with an arrow of time itself.

The covariant quantisation of relativistic particles is reviewed and compared to field quantisation. Then we outline the covariant quantisation of strings, focussing on the novel features compared to relativistic particles which motivate the development of the world-sheet or CFT formalism.

I distinguish between two versions of the black hole information-loss paradox. The first arises from apparent failure of unitarity on the spacetime of a completely evaporating black hole, which appears to be non-globally hyperbolic; this is the most commonly discussed version of the paradox in the foundational and semipopular literature, and the case for calling it `paradoxical' is less than compelling. But the second arises from a clash between a fully statistical-mechanical interpretation of black hole evaporation and the quantum-field-theoretic description used in derivations of the Hawking effect. This version of the paradox arises long before a black hole completely evaporates, seems to be the version that has played a central role in quantum gravity, and is genuinely paradoxical. After explicating the paradox, I discuss the implications of more recent work on AdS/CFT duality and on the `Firewall paradox', and conclude that the paradox is if anything now sharper. The article is written at a (relatively) introductory level and does not assume advanced knowledge of quantum gravity.

String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in this chapter that those two conspicuous characteristics of string physics are related to each other. What links them together is the fact that string theory has no dimensionless-free parameters at a fundamental level. The paper analyzes possible implications of this situation for the long-term prospects of theory building in fundamental physics.